On Kirkwood--Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame
arXiv:2304.14038 · doi:10.1016/j.physa.2023.129208
Abstract
An issue which has attracted increasing attention in contemporary researches are Kirkwood--Dirac quasiprobabilities. List of their use includes many questions of quantum physics. Applications of complex tight frames in quantum information science were recently demonstrated. It is shown in this paper that quasiprobabilities naturally appear in the context of unravelings of a quantum channel. Using vectors of the given tight frame to build principal Kraus operators generates quasiprobabilities with interesting properties. For an equiangular tight frame, we characterize the Hilbert--Schmidt and spectral norms of the matrix consisted of quasiprobabilities. Hence, novel uncertainty relations in terms of Rényi and Tsallis entropies are obtained. New inequalities for characterizing the location of eigenvalues are derived. They give an alternative to estimating on the base of Geršgorin's theorem. A utility of the presented inequalities is exemplified with symmetric informationally complete measurement in dimension two.
14 pages, no figures. Except for the style, matches the journal version
References in corpus (9)
- Conjectured Strong Complementary Information Tradeoff
- Non-equilibrium quantum fluctuations of work
- Improved tripartite uncertainty relation with quantum memory
- Quantum theory of successive projective measurements
- Negative quasiprobabilities enhance phase estimation in quantum-optics experiment
- Kirkwood-Dirac nonclassicality, support uncertainty and complete incompatibility
- Conditions tighter than noncommutation needed for nonclassicality
- On uncertainty relations and entanglement detection with mutually unbiased measurements
- Optimal upper bound of entropic uncertainty relation for mutually unbiased bases